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Ptolemy Inequality

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PtolemysInequality

For a quadrilateral which is not cyclic, Ptolemy's theorem becomes an inequality:

AB×CD+BC×DA>AC×BD.

The Ptolemy inequality is still valid when ABCD is a triangular pyramid (Boomstra 1956-1957).

See also

Pompeiu's Theorem, Ptolemy's Theorem, Quadrilateral, Tweedie's Theorem

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References

Boomstra, W. "Nogmaals de stelling van Pompeïu." Nieuw Tijdschr. Wisk 44, 285-288, 1956-1957.

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Ptolemy Inequality

Cite this as:

Weisstein, Eric W. "Ptolemy Inequality." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PtolemyInequality.html

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